ROBINS, BENJAMIN (1707–1751), mathematician and military engineer, only son of John Robins (1666–1758), a quaker in poor circumstances, was born at Bath in 1707. At an early age he evinced mathematical ability. On leaving school, at the suggestion of Dr. Henry Pemberton [q. v.], to whom a paper by Robins had been shown, he came to London, and within a short time ceased to be a quaker. To prepare for teaching he applied himself to modern languages and the higher mathematics. Without assistance he made a demonstration of the last proposition of Sir Isaac Newton's ‘Treatise of Quadratures,’ which was printed in the ‘Philosophical Transactions of the Royal Society’ (No. 397) in 1727. In the following year Robins published in ‘The Present State of the Republic of Letters’ for May 1728 a masterly confutation of a dissertation by Jean Bernouilli on the laws of motion in bodies impinging on one another. Bernouilli had vainly endeavoured to establish Leibnitz's theory. Robins's admitted victory over the veteran mathematician procured him many scholars, whom he instructed individually and not in classes. He continued for some years teaching pure and applied mathematics and physical science; but, chafing against the confinement entailed by such a life, he gradually gave it up and became an engineer. He now devoted himself to the construction of mills and bridges, the drainage of fens, the making of harbours, and the rendering of rivers navigable. He also studied the principles of gunnery and of fortification.

In this new departure he received considerable assistance from his friend, William Ockenden, and travelled in Flanders in order to gain some acquaintance with the fortification of its strong places. On returning from one of these excursions in 1734, he found learned society in London interested in Bishop Berkeley's treatise against mathematicians, called ‘The Analyst.’ By way of reply, Robins printed in 1735 ‘A Discourse concerning the Nature and Certainty of Sir Isaac Newton's Methods of Fluxions and of Prime and Ultimate Ratios.’ In 1739 he published ‘Remarks on M. Euler's Treatise of Motion; on the Compleat System of Optics written by Dr. Smith, master of Trinity College, Cambridge; and on Dr. Jurin's Discourse of Distinct and Indistinct Vision.’ In the same year he published three able political pamphlets in the tory interest, viz. ‘Observations on the Present Convention with Spain;’ ‘A Narrative of what passed in the Common Hall of the Citizens of London assembled for the election of a Lord Mayor;’ and ‘An Address to the Electors and other Free Subjects of Great Britain occasioned by the late Secession; in which is contained a particular Account of all our Negociations with Spain and their Treatment of us for above ten Years past.’ These pamphlets brought Robins into political notice. The last of the three, published anonymously, was an apology for the defection of certain members of parliament, including Pulteney and Sandys, who, disgusted with the Spanish Convention, declined for a time to attend the House of Commons. By those whose conduct Robins defended, he was appointed secretary of the secret committee nominated by the House of Commons to examine into, and report upon, the past conduct of Walpole. The committee made two reports.

In 1741 Robins was an unsuccessful candidate for the appointment of professor of fortification at the royal military academy recently established at Woolwich. In 1742 he published his best known work, ‘New Principles of Gunnery,’ which he had begun by way of supporting his candidature. This work, the result of many experiments which he had made on the force of gunpowder, and the resisting power of the air to swift and slow motions, was preceded by an account of the progress of modern fortification, of the invention of gunpowder, and of what had already been observed of the theory of gunnery. Robins's book was translated into German by Euler, who wrote a critical commentary on it (Berlin, 1745). Euler's commentary was translated into English, and published by order of the board of ordnance, with remarks and useful tables by Hugh Brown of the Tower of London. ‘New Principles of Gunnery’ was translated into French by Le Roy for the Academy of Sciences of Paris in 1751.

Robins invented the ballistic pendulum, a very ingenious contrivance for measuring the velocity of a projectile, and in 1742 he read a paper on the subject before the Royal Society, of which he was admitted a fellow on 16 Nov. 1727. He also read several papers on gunnery questions, and in 1746 and the following year exhibited to the society various experiments. In 1747 he received the Copley medal.

There appeared in 1747 his ‘Proposal for increasing the Strength of the British Navy by changing all the guns from the eighteen-pounders downwards into others of equal weight but of a greater bore.’ A letter which he addressed on the subject to Admiral Lord Anson was read before the Royal Society on 9 April 1747. In this year the Prince of Orange invited Robins to assist in the defence of Bergen-op-Zoom, then invested by the French, but it was taken on 16 Sept. 1747, just after Robins arrived at the headquarters of the Dutch army.

Lord Anson, who was a friend and patron of Robins, after returning from the voyage round the world in the Centurion, appears to have entrusted to Robins for revision the account of the voyage which had been compiled from the journals by his chaplain, Richard Walter [q. v.] There has been considerable dispute as to whether Robins or Walter wrote the book, which is entitled in the quarto edition of 1748 ‘A Voyage round the World in the Years 1740–1744 by George Anson, Esq.,’ ‘published under his direction by Richard Walter, M.A.’ [see Anson, Georg, Lord Anson.] Dr. James Wilson, who published in 1761 a collected edition of the works of Robins, circumstantially states, on the authority of Glover and Ockenden, friends of Robins, that the printed book was twice as long as Walter's manuscript, which merely consisted of bare extracts from the journals kept during the voyage; that Robins worked them into shape, wrote an introduction, and added dissertations. In an indenture between Robins and the booksellers, John and Paul Knapton, Robins was treated as the sole proprietor. On 22 Oct. 1749 Lord Anson wrote to Robins from Bath to ask whether he intended to publish the second volume before he left England, and Lady Anson, in a letter to Dr. Birch, asks if Robins's second volume is ready. On the other hand, the widow and children of Walter claimed that the work was written by him. It seems probable that Robins revised and edited the work, and was especially entrusted with the second volume, containing the nautical observations; the manuscript he took with him to India, and when he died in that country it could not be found.

Robins's reputation as a pamphleteer caused him to be employed on an apology for the battle of Prestonpans, which formed a preface to the ‘Report of the Proceedings and Opinion of the Board of General Officers on their Examination into the conduct of Lieutenant-general Sir John Cope,’ 1749. On 4 May 1749 a paper by Robins on ‘Rockets and the Heights to which they ascend’ was read before the Royal Society, and on 13 Dec. 1750 an account of some experiments made by Robins and others on the flight of rockets. By the favour of Lord Anson, Robins was able to continue his experiments in gunnery, the results of which were published from time to time in the ‘Philosophical Transactions.’ He also contributed to the improvement of the Royal Observatory at Greenwich by inducing Lord Anson to procure a second mural quadrant and other instruments.

In 1749 Robins was given the choice of going to Paris as one of the British commissioners for adjusting the boundaries of Acadia or of going to India as engineer-general to repair the forts of the East India Company. He chose the latter, being appointed in Dec. 1749 chief engineer and captain of the train of the Madras artillery. His precedence in India was to rank with the third in council. He was entrusted with the appointment of all his subordinates, and given ample funds. Lord Anson expressed regret that he was leaving England. Robins set out at Christmas 1749, taking with him a complete set of astronomical instruments, and also instruments for making observations and experiments. After a narrow escape from shipwreck, he arrived at Madras on 13 July 1750. He immediately designed complete projects for Fort St. David and the defence of Madras. In September he was attacked by fever. In 1751 he fell into a low state of health, anddied, unmarried, on 29 July 1751 at Fort St. David, with the pen in his hand while drawing up a report for the board of directors.

In manner unostentatious, without pedantry or affectation, Robins was a lively and entertaining conversationalist. He was always ready to communicate to others the result of his studies and labours. He left the publication of his works to his friend Martin Folkes, president of the Royal Society; but Folkes, owing to a paralytic attack, was unable to act, and Thomas Lewis, Robins's executor, entrusted the work to Dr. James Wilson, who, in 1761, published ‘Mathematical Tracts’ (London, 2 vols. 8vo), containing ‘Principles of Gunnery,’ together with many other pieces and a memoir of Robins. The book became a text-book, and Dr. Charles Hutton issued a new edition in 1805. Besides the papers mentioned, he contributed to the ‘Transactions of the Royal Society’ two on the ‘Resistance of the Air, together with the Method of computing the Motions of Bodies projected in that Medium,’ read June 1746; ‘An Account of a Book entitled “New Principles of Gunnery,” containing the Determination of the Force of Gunpowder and an Investigation of the Resisting Power of the Air to Swift and Slow Motions’ (No. 469, p. 437); ‘Experiments showing that the Electricity of Glass disturbs the Mariner's Compass and also nice Balances,’ 1746; ‘An Account of Experiments relating to the Resistance of the Air,’ 1747; ‘On the Force of Gunpowder, together with the Computation of the Velocities thereby communicated to Military Projectiles,’ 1747; ‘A Comparison of the Experimental Ranges of Cannon and Mortars, with the Theory contained in preceding Papers,’ 1751; ‘A Letter to the President of the Royal Society in answer to his, enclosing a Message from the Chevalier d'Ossorio, Envoy of the King of Sardinia,’ 7 Jan. 1747; ‘Of the Nature and Advantages of Rifled-barrel Pieces,’ July 1747.